/*
 * Modelling Viral Dynamics In Vivo
 * 
 * Model Status
 * 
 * This model contains time delays and is unsuitable for solution
 * using CellML. There are additional problems with the model,
 * but the presence of time delays rendered these superfluous.
 * 
 * Model Structure
 * 
 * Clinical studies of drug therapy in patients infected with HIV-1
 * or the hepatitis B virus provide the opportunity for estimating
 * the kinetic constants of virus replication in vivo. Treatment
 * of HIV-1 with protease inhibitors results in the decline of
 * free virus in several distinct phases: Initially the plasma
 * virus load remains virtually unchanged, then after this initial
 * delay, the plasma load declines exponentially, due to the decreased
 * virus synthesis in infected cells, and also due to the clearance
 * of free virus particles. Finally, the rate of virus decline
 * decreases, and the viral load may even begin to increase again
 * as the virus evolves a resistance to the protease inhibitor.
 * 
 * This publication by Herz et al. quickly followed an article
 * by Perelson et al. (1996) in which they developed a mathematical
 * model of HIV-1 dynamics in vivo based on their experimental
 * data. In this current publication, Herz et al. develop a new
 * model that provides a description of HIV-1 dynamics, including
 * the effects of an intracellular delay (the period between infection
 * of a cell and the production of new virus particles). This model
 * accounts for the effects of a protease inhibitor on the rate
 * of viral synthesis (see below), and it has been encoded in CellML
 * and can be downloaded in various formats in .
 * 
 * The complete original paper reference is cited below:
 * 
 * Limitations on estimates of intracellular delay and virus decay,
 * Andreas V. M. Herz, Sebastian Bonhoeffer, Roy M. Anderson, Robert
 * M. May, and Martin A. Nowak, 1996, Proceedings of the National
 * Academy of Science, USA, 93, 7247-7251. PubMed ID: 8692977
 * 
 * cell diagram
 * 
 * [[Image file: herz_1996.png]]
 * 
 * Schematic summary of the dynamics of viral infection in vivo.
 * 
 * Model simulations revealed that the half-life of the infected
 * cells can be calculated with reasonable accuracy from clinical
 * data. However, the remaining parameters can not be accurately
 * predicted from the current model, more data is needed.
 */

import nsrunit;
// Warning: unit conversion turned off due to unit errors in 2 equation(s)
unit conversion off;
unit per_mm3=1E9 meter^(-3);
unit hour=3600 second^1;
unit day=86400 second^(-1);
unit first_order_rate_constant=1.1574074E-5 second^1;

math main {
	//Warning:  the following variables were set 'extern' or given
	//  an initial value of '0' because the model would otherwise be
	//  underdetermined:  x, lamda, beta, vI, y, a_, v, k
	realDomain time day;
	time.min=0;
	extern time.max;
	extern time.delta;
	real x(time) per_mm3;
	//Warning:  Assuming zero initial condition; nothing provided in original CellML model.
	when(time=time.min) x=0;
	extern real lamda first_order_rate_constant;
	extern real beta first_order_rate_constant;
	real vI(time) per_mm3;
	//Warning:  Assuming zero initial condition; nothing provided in original CellML model.
	when(time=time.min) vI=0;
	real y(time) per_mm3;
	//Warning:  Assuming zero initial condition; nothing provided in original CellML model.
	when(time=time.min) y=0;
	real tau hour;
	tau=12.0;
	real a first_order_rate_constant;
	a=0.5;
	extern real a_ first_order_rate_constant;
	real v(time) per_mm3;
	//Warning:  Assuming zero initial condition; nothing provided in original CellML model.
	when(time=time.min) v=0;
	extern real k first_order_rate_constant;
	real u first_order_rate_constant;
	u=3.0;

	// <component name="environment">

	// <component name="x">
	x:time=(lamda-(x+beta*x*vI));

	// <component name="y">
	y:time=(beta*(time-tau)*x*(time-tau)*vI*(time-tau)*exp(a_*tau)-a*y);

	// <component name="v">
	v:time=(k*y-u*v);

	// <component name="vI">
	vI:time=((-1)*(u*vI));

	// <component name="kinetic_parameters">
}